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Q.

The total cost $C (x)$ in rupees associated with production of $x$ units of an item is given by $C (x) = 0.005 x^{3} - 0.02 x^{2} + 30 x + 500$ . Find the marginal cost when $3$ units are produced (marginal cost is the rate of change of total cost)

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Detailed Solution

Total cost $C (x) = 0.005 x^{3} - 0.02 x^{2} + 30 x + 500$

Marginal cost $M = \frac{d}{d x} C (x)$

$= 0.015 x^{2} - 0.04 x + 30$

$M_{at x = 3} = 0.015 (3)^{2} - 0.04 (3) + 30 = 30.015$

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